Rotational Motion Question 33
Question: A particle of mass 2 kg is moving such hat at time t, its position, in meter, is given by $ \overset{\to }{\mathop{r}}(t)=5\hat{i}-2{t \hat {2}}\hat{j}. $ The angular momentum of the particle at $ t=2s $ about the origin in kg $ {m \hat {-2}} $ $ {s \hat {-2}} $ is:
[JEE ONLINE 23-04-2013]
Options:
A) $ -80\hat{k} $
B) $ ( 10\hat{i}-16\hat{j} ) $
C) $ -40\hat{k} $
D) $ 40\hat{k} $
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] Angular momentum
$\overrightarrow {P}=m\overrightarrow{v}=md\overrightarrow{r}dt=2(−4t) \hat j=−16 \hat j $
putting t=2 $\overrightarrow{}r=5 \hat i−8 \hat j\overrightarrow{L}= \overrightarrow{r }x \overrightarrow{p}$
Substituting,$\overrightarrow{L}= (5 \hat i−8 \hat j) x (−16 \hat j)\overrightarrow{L}=−80 \hat k$
